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Mathbox for Giovanni Mascellani |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > alrimii | Structured version Unicode version |
Description: A lemma for introducing a universal quantifier, in inference form. (Contributed by Giovanni Mascellani, 30-May-2019.) |
Ref | Expression |
---|---|
alrimii.1 |
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alrimii.2 |
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alrimii.3 |
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alrimii.4 |
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Ref | Expression |
---|---|
alrimii |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alrimii.1 |
. . 3
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2 | alrimii.2 |
. . . 4
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3 | alrimii.3 |
. . . 4
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4 | 2, 3 | sylibr 212 |
. . 3
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5 | 1, 4 | alrimi 1816 |
. 2
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6 | nfsbc1v 3314 |
. . 3
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7 | alrimii.4 |
. . 3
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8 | sbceq2a 3306 |
. . 3
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9 | 6, 7, 8 | cbval 1981 |
. 2
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10 | 5, 9 | sylib 196 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1955 ax-ext 2432 |
This theorem depends on definitions: df-bi 185 df-an 371 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2604 df-sbc 3295 |
This theorem is referenced by: (None) |
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